Expected publication date is January 11,
2004
Description
Symbolic dynamics originated as a tool for
analyzing dynamical
systems and flows by discretizing space as
well as time. The
development of information theory gave impetus
to the study of
symbol sequences as objects in their own
right. Today, symbolic
dynamics has expanded to encompass multi-dimensional
arrays of
symbols and has found diverse applications
both within and beyond
mathematics.
This volume is based on the AMS Short Course
on Symbolic Dynamics
and its Applications. It contains introductory
articles on the
fundamental ideas of the field and on some
of its applications.
Topics include the use of symbolic dynamics
techniques in coding
theory and in complex dynamics, the relation
between the theory
of multi-dimensional systems and the dynamics
of tilings, and
strong shift equivalence theory.
Contributors to the volume are experts in
the field and are clear
expositors. The book is suitable for graduate
students and
research mathematicians interested in symbolic
dynamics and its
applications.
Contents
S. G. Williams -- Introduction to symbolic
dynamics
B. Marcus -- Combining modulation codes and
error correcting
codes
P. Blanchard, R. L. Devaney, and L. Keen
-- Complex dynamics and
symbolic dynamics
D. Lind -- Multi-dimensional symbolic dynamics
E. A. Robinson, Jr. -- Symbolic dynamics
and tilings of mathbb{R}^d
J. B. Wagoner -- Strong shift equivalence
theory
Index
Details:
Series: Proceedings of Symposia in Applied
Mathematics,Volume: 60
Publication Year: 2003
ISBN: 0-8218-3157-7
Paging: approximately 168 pp.
Binding: Hardcover
Expected publication date is January 1, 2004
"This book not only provides a lot of
solid information
about real analysis, it also answers those
questions which
students want to ask but cannot figure how
to formulate. To read
this book is to spend time with one of the
modern masters in the
subject."
-- Steven G. Krantz, Washington University,
St. Louis
"T. W. Korner's A Companion to Analysis
is a welcome
addition to the literature on undergraduate-level
rigorous
analysis. It is written with great care with
regard to both
mathematical correctness and pedagogical
soundness. Korner shows
good taste in deciding what to explain in
detail and what to
leave to the reader in the exercises scattered
throughout the
text. And the enormous collection of supplementary
exercises in
Appendix K, which comprises almost one-third
of the whole book,
is a valuable resource for both teachers
and students.
"One of the major assets of the book
is Korner's very
personal writing style. By keeping his own
engagement with the
material continually in view, he invites
the reader to a
similarly high level of involvement. And
the witty and erudite
asides that are sprinkled throughout the
book are a real pleasure."
-- Gerald Folland, University of Washington,
Seattle
Description
Many students acquire knowledge of a large
number of theorems and
methods of calculus without being able to
say how they work
together. This book provides those students
with the coherent
account that they need. A Companion to Analysis
explains the
problems that must be resolved in order to
procure a rigorous
development of the calculus and shows the
student how to deal
with those problems.
Starting with the real line, the book moves
on to finite-dimensional
spaces and then to metric spaces. Readers
who work through this
text will be ready for courses such as measure
theory, functional
analysis, complex analysis, and differential
geometry. Moreover,
they will be well on the road that leads
from mathematics student
to mathematician.
With this book, well-known author Thomas
Korner provides able and
hard-working students a great text for independent
study or for
an advanced undergraduate or first-level
graduate course. It
includes many stimulating exercises. An appendix
contains a large
number of accessible but non-routine problems
that will help
students advance their knowledge and improve
their technique.
Contents
The real line
A first philosophical interlude
Other versions of the fundamental axiom
Higher dimensions
Sums and suchlike
Differentiation
Local Taylor theorems
The Riemann integral
Developments and limitations of the Riemann
integral
Metric spaces
Complete metric spaces
Contraction mappings and differential equations
Inverse and implicit functions
Completion
Appendices
Executive summary
Exercises
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,
Volume: 62
Publication Year: 2004
ISBN: 0-8218-3447-9
Paging: approximately 608 pp.
Binding: Hardcover
Expected publication date is January 1, 2004
Description
This volume covers material presented by
invited speakers at the
AMS special session on Riemannian and Lorentzian
geometries held
at the annual Joint Mathematics Meetings
in Baltimore. Topics
covered include classification of curvature-related
operators,
curvature-homogeneous Einstein 4-manifolds,
linear stability/instability
singularity and hyperbolic operators of spacetimes,
spectral
geometry of holomorphic manifolds, cut loci
of nilpotent Lie
groups, conformal geometry of almost Hermitian
manifolds, and
also submanifolds of complex and contact
spaces.
This volume can serve as a good reference
source and provide
indications for further research. It is suitable
for graduate
students and research mathematicians interested
in differential
geometry.
Contents
K. Abe, D. Grantcharov, and G. Grantcharov
-- On some complex
manifolds with torus symmetry
M. J. S. Ashley and S. M. Scott -- Curvature
singularities and
abstract boundary singularity theorems for
space-time
A. Derdzinski -- Curvature-homogeneous indefinite
Einstein
metrics in dimension four: The diagonalizable
case
P. E. Ehrlich, Y.-T. Jung, J.-S. Kim, and
S.-B. Kim -- Jacobians
and volume comparison for Lorentzian warped
products
B. Fiedler and P. Gilkey -- Nilpotent Szabo,
Osserman and Ivanov-Petrova
pseudo-Riemannian manifolds
P. B. Gilkey, R. Ivanova, and I. Stavrov
-- Jordan Szabo
algebraic covariant derivative curvature
tensors
A. D. Helfer -- Differential topology, differential
geometry, and
hyperbolic operators
C. Jang and P. E. Parker -- Examples of conjugate
loci of
pseudoriemannian 2-step nilpotent Lie groups
with nondegenerate
center
R. G. McLenaghan, R. G. Smirnov, and D. The
-- Group invariant
classification of orthogonal coordinate webs
J. H. Park -- Spectral geometry and the Kaehler
condition for
Hermitian manifolds with boundary
P. Rukimbira -- Energy, volume and deformation
of contact metrics
R. Sharma -- Holomorphically planar conformal
vector fields on
almost Hermitian manifolds
B. D. Suceava -- Fundamental inequalities
and strongly minimal
submanifolds
M. Tanimoto -- Linear perturbations of spatially
locally
homogeneous spacetimes
M. M. Tripathi -- Certain basic inequalities
for submanifolds in (kappa,mu)-spaces
Details:
Series: Contemporary Mathematics,Volume:
337
Publication Year: 2003
ISBN: 0-8218-3379-0
Paging: approximately 202 pp.
Binding: Softcover
Expected publication date is January 11, 2004
Description
This volume contains the expanded lecture
notes of courses taught at the Emile Borel
Centre of the Henri Poincare Institute (Paris).
In the book, leading experts introduce recent
research in their fields. The unifying theme
is the study of heat kernels in various situations
using related geometric and analytic tools.
Topics include analysis of complex-coefficient
elliptic operators, diffusions on fractals
and on infinite-dimensional groups, heat
kernel and isoperimetry on Riemannian manifolds,
heat kernels and infinite dimensional analysis,
diffusions and Sobolev-type spaces on metric
spaces, quasi-regular mappings and p-Laplace
operators, heat kernel and spherical inversion
on SL_2(C), random walks and spectral geometry
on crystal lattices, isoperimetric and isocapacitary
inequalities, and generating function techniques
for random walks on graphs.
This volume is suitable for graduate students
and research
mathematicians interested in random processes
and analysis on
manifolds.
Contents
P. Auscher -- Some questions on elliptic
operators
M. T. Barlow -- Heat kernels and sets with
fractal structure
A. Bendikov and L. Saloff-Coste -- Brownian
motion on compact
groups of infinite dimension
T. Coulhon -- Heat kernel and isoperimetry
on non-compact
Riemannian manifolds
B. K. Driver -- Heat kernels measures and
infinite dimensional
analysis
A. Grigor'yan -- Heat kernels and function
theory on metric
measure spaces
P. Hajlasz -- Sobolev spaces on metric-measure
spaces
I. Holopainen -- Quasiregular mappings and
the p-Laplace operator
J. Jorgenson and S. Lang -- Spherical inversion
on SL_2(C)
M. Kotani and T. Sunada -- Spectral geometry
of crystal lattices
V. Maz'ya -- Lectures on isoperimetric and
isocapacitary
inequalities in the theory of Sobolev spaces
S. Semmes -- Some topics related to analysis
on metric spaces
K.-T. Sturm -- Probability measures on metric
spaces of
nonpositive curvature
W. Woess -- Generating function techniques
for random walks on
graphs
Details:
Series: Contemporary Mathematics, Volume:
338
Publication Year: 2003
ISBN: 0-8218-3383-9
Paging: 424 pp.
Binding: Softcover
Expected publication date is January 7, 2004
Description
Since the publication of the first edition
in 1986 by Academic
Press, this book has served as one of the
few available on the
classical Adams spectral sequence and the
best account on the
Adams-Novikov spectral sequence. This new
edition has been
updated in many places, especially the final
chapter, which has
been completely rewritten with an eye toward
future research in
the field. It remains the definitive reference
on the stable
homotopy groups of spheres.
The first three chapters introduce the homotopy
groups of spheres
and take the reader from the classical results
in the field
though the computational aspects of the classical
Adams spectral
sequence and its modifications, which are
the main tools
topologists have to investigate the homotopy
groups of spheres.
Nowadays, the most efficient tools are the
Brown-Peterson theory,
the Adams-Novikov spectral sequence, and
the chromatic spectral
sequence, a device for analyzing the global
structure of the
stable homotopy groups of spheres and relating
them to the
cohomology of the Morava stabilizer groups.
These topics are
described in detail in Chapters 4 to 6. The
revamped Chapter 7 is
the computational payoff of the book, yielding
a lot of
information about the stable homotopy group
of spheres.
Appendices follow, giving self-contained
accounts of the theory
of formal groups laws and the homological
algebra associated with
Hopf algebras and Hopf algebroids.
The book is intended for anyone wishing to
study computational
stable homotopy theory. It is accessible
to graduate students
with a knowledge of algebraic topology and
recommended to anyone
wishing to venture into the frontiers of
the subject.
Contents
An introduction to the homotopy groups of
spheres
Setting up the Adams spectral sequence
The classical Adams spectral sequence
BP-theory and the Adams-Novikov spectral
sequence
The chromatic spectral sequence
Morava stabilizer algebras
Computing stable homotopy groups with the
Adams-Novikov spectral
sequence
Hopf algebras and Hopf algebroids
Formal group laws
Tables of homotopy groups of spheres
Bibliography
Index
Details:
Series: AMS Chelsea Publishing
Publication Year: 2003
ISBN: 0-8218-2967-X
Paging: 395 pp.
Binding: Hardcover